Hospitals run more machine learning on GPUs while the carbon footprint of grid electricity rises and falls through the day. Using a computer simulation, we compare $13$ scheduling rules on mixed GPU hardware, with synthetic patient-style jobs, urgency tiers, and time-of-day carbon traces. We do not study patient outcomes; every percentage we report is a simulator queue number, not a clinical finding. We ask whether running non-urgent jobs overnight is almost as good as a richer rule that mixes urgency and carbon (CUCA at weight 0.45, written CUCA$_{0.45}$). The comparison keeps carbon reduction secondary to clinical priority and deadline compliance, so each policy is judged on both average kg CO$_2$e and missed-deadline behavior. CarbonGreedy and CarbonShift are carbon-first stress tests that demonstrate how poorly wrong vendor presets can disrupt clinical priorities, and are not meant for production. Numbers are averages over many test settings, with wide run-to-run spread and no statistical adjustment, so headline ratios are exploratory. On an eight-GPU baseline, the overnight rule closes about $78\%$ of the carbon gap between urgency-only and CUCA$_{0.45}$ while missing fewer urgent deadlines than either. CarbonShift lets about $46\%$ of the most urgent jobs miss their deadline; this is simulated queueing, not bedside harm. At $48$ jobs per hour, the carbon footprints almost tie, yet the overnight rule still misses fewer urgent deadlines. A geography test, where regions share one daily carbon shape with only timezone shifts, trims under one percentage point of average carbon; a twelve-hour routine window saves a little carbon for CUCA$_{0.45}$ but raises overall missed deadlines. Overnight batching stays competitive on average modelled carbon; carbon-only rules belong only in stress tests.